Comptes Rendus
no. 6
Number theory/Algebra
Trace formula for Witt vector rings
[Formule de trace pour les anneaux vectoriels de Witt]

Présenté par : the Editorial Board

Benzaghou Benali1 ; Mokhfi Siham2
1 USTHB, Faculté des mathématiques, B.P. 32, El Alia, 16111 Alger, Algeria
2 Université Saad-Dahleb, Faculté des sciences, B.P. 270, route de Soumâa, 09000 Blida, Algeria
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 601-606.

On commence par généraliser les séries exponentielles de Pulita. Ensuite, on se sert de cette généralisation pour établir un analogue de la formule de trace de Dwork sur des anneaux de Witt.

We commence by giving a generalisation of Pulita exponential series. We then use these series to establish an analog of the trace formula for Witt vector rings.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.11.014
Benzaghou Benali 1 ; Mokhfi Siham 2

1 USTHB, Faculté des mathématiques, B.P. 32, El Alia, 16111 Alger, Algeria
2 Université Saad-Dahleb, Faculté des sciences, B.P. 270, route de Soumâa, 09000 Blida, Algeria 
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     title = {Trace formula for {Witt} vector rings},
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     pages = {601--606},
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     doi = {10.1016/j.crma.2016.11.014},
     language = {en},
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Benzaghou Benali; Mokhfi Siham. Trace formula for Witt vector rings. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 601-606. doi : 10.1016/j.crma.2016.11.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.11.014/

[1] B. Benzaghou; S. Mokhfi Trace formula for Witt vector rings, 2016 (Arxiv) | arXiv

[2] R. Blache Stickelberger theorem for p-adic Gauss sums, Acta Arith., Volume 118 (2005) no. 1, pp. 11-26

[3] G. Christol Modules différentiels et équations différentielles p-adiques, Queen's Papers in Pure and Applied Mathematics, vol. 66, Queen's University, Kingston, ON, Canada, 1983 (vi+218 pp.)

[4] B. Dwork On the rationality of the zeta function of an algebraic variety, Amer. J. Math., Volume 82 (1960), pp. 631-648

[5] M. Hazewinkel Witt vectors. Part I, Handbook of Algebra, vol. 6, Elsevier/North-Holland, Amsterdam, 2009, pp. 319-472 (section 4H)

[6] K.S. Kedlaya Convergence polygons for connections on nonarchimedean curves, 2015 (Arxiv) | arXiv

[7] J. Lubin; J. Tate Formal complex multiplication in local fields, Ann. of Math. (2), Volume 81 (1965), pp. 380-387

[8] A. Pulita Rank one solvable p-adic differential equations and finite Abelian characters via Lubin–Tate groups, Math. Ann., Volume 337 (2007) no. 3, pp. 489-555

[9] W.H. Schikof Ultrametric Calculus, Cambridge Studies in Advanced Mathematics, vol. 4, Springer-Verlag, New York, 1973

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